An Andy Little strike just before the interval was all that separated the two sides on a sunny but blustery day at Station Park.
Rangers were sent crashing out of the Scottish League Cup at the same venue the last time the two sides met in August.
And McCoist refused to be too hard on his players after securing the victory this time despite some dissenting voices from the travelling support.
He said: "I wasn't happy with the performance and I agree with the fans.
"We told the players that but I can sympathise with the players because of the wind.
"As disappointed as we all are with the performance, I would certainly cut the players some slack because of it.
"The conditions played a massive part in the way the game was played and sadly for the fans there wasn't a lot of good football."
He added: "The wind was horrendous and all over the place. You saw the amount of times the ball either hung up or went flying forward.
"It didn't help the flow of the game and didn't help either of us pass the ball.
"When you have conditions like that you have to adapt to them. Both teams attempted to do that as best they could.
"I thought we had the better chances but Forfar still had a threat, particularly late in the second half."
Rangers struggled on the road in the early part of last season and McCoist admits this was a game they may not have won this time last year.
He said: "We knew it would be tough coming here. We didn't need a reminder and got the game we expected.
"Forfar were spirited and very professional so we're delighted to go back down the road with the three points.
"We probably won't have to earn another three points like that this season. That was as competitive a fixture as we've had in a long, long time.
"I'll watch the game again but I'm not sure we would have won this a year ago."
Meanwhile, McCoist hopes to find out in the next 24 hours if former Hearts skipper Marius Zaliukas has accepted an offer to join the Light Blues after impressing during a trial period.
He said: "I'll give Marius a phone either tonight or tomorrow morning. I'll have a chat with him and see what he's got to say."
Reflecting on the match, Forfar assistant boss Ian Campbell said: "The goal we lost wasn't acceptable, not at any level of football.
"But I thought we played well and we are disappointed not to take something from the game. Our finishing and set-pieces were not good enough.
"I don't think Rangers created a lot of chances and we coped with them pretty well.
"But we didn't put the ball in the net when the chances came along for us.
"We worked hard and were organised and we will take a lot out of the game. Hopefully we can take this on now to the rest of the league."
- Sports & Recreation
- Scottish League Cup